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Seminario di Probabilità e Finanza matematica: “Entropic repulsion for the occupation-time field of random interlacements by disconnection”

Giovedì 27 Febbraio 2020, ore 11:30 - Aula Seminari 430 - Alberto Chiarini

ARGOMENTI: Seminari

Giovedì 27 Febbraio 2020 alle ore 11:30 in Aula Seminari 430, Alberto Chiarini (TU Eindhoven) terrà un seminario dal titolo “Entropic repulsion for the occupation-time field of random interlacements by disconnection”.

Abstract
The model of random interlacements was introduced in 2007 by A.-S. Sznitman, motivated by questions about the disconnection of discrete cylinders or tori by the trace of simple random walk. Since then, it has gained popularity among probabilists due to its percolative properties and also because of its connections to the free field. Random interlacements on transient graphs can be constructed as a Poisson point process of doubly infinite trajectories. After reviewing this model, we will focus on the rare event that these trajectories disconnect a macroscopic body from infinity, in the strongly percolative regime. We will ask the following question: What is the most efficient way for random interlacements to enforce such disconnection? In other words, how do the trajectories of random interlacements look like conditionally on disconnection?